CAMBRIDGE — Harvard University’s controversial clampdown on single-gender clubs came under double-barreled legal fire Monday as six sororities and fraternities filed a pair of sex discrimination lawsuits alleging the school used threats and intimidation against students and violated their rights to free association.

Harvard’s policy of penalizing students who join single-gender clubs has virtually eliminated all-female social organizations and shut down their gathering spaces, the plaintiffs said in a federal lawsuit that was filed along with a separate Massachusetts suit.

“Women and their former all-female social clubs have suffered the most,” the federal lawsuit said. “A Harvard undergraduate could join the American Nazi party, or could create an off-campus undergraduate chapter of the Ku Klux Klan, without running afoul of the sanctions policy, or any other Harvard student-conduct policy. Those groups may be heinous but they are co-ed, so under Harvard’s rules, its students may belong without any threat of sanction.”

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Three individual male students are also part of the suits, although they are unnamed for fear of retribution from Harvard, their lawyers said.

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The legal challenge serves as a dramatic postscript to a multiyear fight at Harvard between the administration and a group of off-campus, all-male social groups known as final clubs. It also marks the second recent high-profile lawsuit against the university. Harvard is awaiting a federal district court judge’s ruling in Boston on a lawsuit alleging that it discriminates against Asian-American applicants.

Harvard declined to comment on the new legal challenges Monday. In the past, the university has said that the elite clubs foster an exclusionary environment on campus and that their raucous parties have contributed to unsafe situations leading to sexual assault.

This claim has been challenged by many students and alumni, and the federal lawsuit filed Monday contains perhaps the most detailed account to date of the behind-the-scenes debate between the administration and the clubs.

According to that lawsuit, the relationship between Harvard and the clubs was “cordial” for several decades. But Harvard targeted the final clubs and single-gender organizations in 2014 after Rakesh Khurana became the dean of the undergraduate college and the US Department of Education’s Office of Civil Rights received a complaint over how the college handled allegations of sexual harassment and assault.

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The lawsuit alleges that in a series of meetings Khurana had with club officials, he attempted to force the final clubs to admit women.

In May 2015, the suit says, Khurana held what was billed as a typical meeting to ensure the groups were aware of the latest school policies on alcohol and sexual assault.

Instead, Khurana allegedly told club representatives at that meeting that the university had already decided the clubs would have to go co-ed. At that meeting, according to the suit, Khurana waved a sheet of paper in the air that he said contained accounts of sexual assault.

“Khurana said that the papers in his hand were very embarrassing to the clubs and that he could not guarantee that they would not be leaked,” the lawsuit says. “But, Khurana said, if some clubs became co-ed — systematically and soon — that would help the situation. It was an unmistakable threat.”

Under the Harvard policy, starting with the Class of 2021, students who join a single-gender club are barred from leadership positions such as being captain of a varsity athletic team or receiving a college endorsement for a prestigious graduate fellowship or scholarships, including the Rhodes.

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The final clubs are not among organizations formally suing Harvard, but some of them have collaborated with the legal challenge and are providing financial support, according to the North American Interfraternity Conference.

The sororities argue that they were collateral damage in the university’s mission to eliminate the male-only final clubs because Harvard created a policy that punishes not just the male clubs but all single-gender, off-campus clubs.

“Harvard attempted to tell the female students what was good for them without bothering to ask them,” Rebecca Ramos, a 2017 Harvard graduate and former chapter president of the college’s Delta Gamma sorority, said at a news conference in Cambridge.

In 2014, Harvard had nine sororities and all-female final clubs. But as a result of the sanctions, only one still exists, according to the lawsuits. The remaining have closed or become co-ed. Sororities had to break ties with the national organizations that supported them, and many saw their membership plummet.

The federal suit alleges that the university violated students’ right to freedom from sex discrimination under the well-known Title IX statute. The law bars discrimination on the basis on sex.

The plaintiffs for the federal suit are Kappa Alpha Theta and Kappa Kappa Gamma, international sororities; Sigma Chi and Sigma Alpha Epsilon, international fraternities; Sigma Alpha Epsilon — Massachusetts Gamma, the local chapter; and three current Harvard students who are members of male clubs.

The federal lawsuit points out that the new policy has also affected such groups as the all-female Radcliffe Choral Society and the all-male Harvard Glee Club and also would punish students who join groups including the Knights of Columbus, an all-male Catholic organization.

The suit also describes how policy caused harm to the three individual male plaintiffs, allegedly damaging their reputation, job opportunities, and ability to continue their leadership roles in the single-gender clubs.

The state suit, filed by three women’s organizations, asserts that the university interfered with students’ right to free association and equal treatment based on sex, as protected by the state Constitution.

The plaintiffs in the state suit are Delta Gamma and Alpha Phi, international sororities; and Alpha Phi — Iota Tau, the Cambridge chapter.

The lawsuits seek to bar Harvard from enforcing the sanctions policy.

They are the latest attempt by the single-gender organizations to fight Harvard’s policy. The final clubs, fraternities, and sororities have also lobbied Congress to protect single-sex organizations. But with Democrats soon taking control of the House of Representatives, those efforts may stall.

“We are going to fight this every avenue we can,” said Judson Horras, the president of the North American Interfraternity Conference. “This was our last resort and we knew we had to do this.”